Search results

True.

^ No sorry sasquatch, I understand what you were trying to do and my fault for not distinguishing that from what I said. It wasn't my intention to say that you were wrong or being intentionally misguiding lol :p I was just trying to make a point about Newton's Method, I probably shouldn't have...

1) There is a reason I italicised the word "defined" in my last post sasquatch as I knew something of the nature of your statement 1 would come up: It is a definition - a logically 'sufficient' formulation of the concept of GPE so as to be reconcilable with the quantatitive theory behind it...

^ I think you know exactly what geometry we're dealing with here Templar. Saying that lines meet at infinity does not make any comment on them being parallel or not, and thus can be easily interpretted as an admission that the lines are parallel (which they are not) - one can easily say that...

^ But I think you have to be carefully though, when criticising "Australian" HS physics, since different states and territories have different assessable outcomes and curricula. This applies to maths as well - e.g. in NSW there is no evidence of statistics, or elements of linear algebra (e.g...

^ When you are required to solve a differential equation, it means you are to produce a function of the independent variables which satisfies the differential equation. e.g. the solution to the differential equation y'(x) = 2x, is given by y = x2 + C where y is the dependent variable, and x the...

Hi onebytwo, Question 1: I think this is a celebrated inequality, so am certain that there are probably many different proofs of this out there on the net waiting to be looked up (though I've not seen any myself), but I just had a go at it and here's how I approached it, adhereing to only...

^ Cheating :p ? Well, at least we don't need to use up space on the 'cheat sheets' to write up induction proof-formulae ;) , so it's good for something right?

I have to agree with Templar on this. (Though I disagree with his comment about "then they much must meet at infinity" since meeting at infinity is essentially a concession that they are indeed parallel for all practical purposes, which they certainly are not.) Your example is simply a...

^ Although it's essentially the same method, using z/(z-3) is really taking the long way of doing it instead of (1 - 3/z), particularly in the solution of the roots where one would usually be required to express them in mod-arg form instead of an inverted complex numbers added to a real constant.

I'm not sure if any of the subsequent posts actually answered your question, but I think I understand where you're coming from as I had the same conceptual difficulties with induction as well in year 11. Please tell me if I am wrong, but I think the crux of what you're asking lies in the...

But what's with that though? Clearly it's just mathematicians practicing hubris again... Can't Physics and Mathematics just get along on the HS level :) ?

1) Newton's formula is a contraction mapping on the metric space R1 with the standard metric for appropriate functions and carefully chosen initial value inputs. - It will never give you an exact root, unless your intial input is the root. 2) Taking 0.999994021 to be 1 as a root (or even...

Yes to the best of my knowledge, this is in fact a standard 4u question. It has been examined before in HSC exams as well as holding presence in exercises in many standard 4u textbooks.

Grave apologies people... made a terrible mistake in the bolded lines above ^ :( . Thankfully no-one has complained of it yet. The quoted line: "" pi/2 = Tan-1(#) + Tan-1(1/#) "" should in fact read: pi/2+- = Tan-1(#) + Tan-1(1/#) where I've used the notation x+- to denote "plus or...

http://community.boredofstudies.org/14/mathematics-extension-2/115239/solve.html has a similar question in which the solution to getting your desired result is exactly the same save for a few different algebraic manipulations along the way.

Dear onebytwo, hoping this isn't too late to help. First, begin with the following identity: (from memory, I did this last year so you probably would know it already but just in case you didn't I have laid out the proof in the appendix at the end of this post) 1 - Cis@ = (2(1- Cos@))1/2...

^ Thanks Riviet. Must be that mental-block I was talking about huh :rolleyes: ...

People sometimes have mental-blocks which may be attributed to many factors such as deprivation of sleep, general fatigue, or bouts of depression, etc... Ergo, I don't like to jump to the conclusion that a 4unit student temporarily unable to complete a 2unit mathematics problem must imply an...

∫Sqrt(16 - x2)/x2 dx Let x = 4Sin(u) , dx = 4Cos(u) du -----> u = ArcSin(x/4) I = (1/4)∫Cos2u/Sin2u du = (1/4)∫Cot2u du = (1/4)∫(Csc2u - 1) du Note that d(Cot(u))/du = -Csc2u in much the similar way that d(Tan(u))/du = Sec2u [It's a good idea to learn these differentials off by...